Spokeswoman Kanze Dena says the four were found positive following a mass testing of staff on Thursday last week.
They have been admitted to the Kenyatta University Teaching Referral Hospital and their families are being tested.
Dena said the Kenyan president and his family are safe and free of the disease.
Kenya health ministry has announced it will start home care of asymptotic COVID-19 cases, as the country's hospitals are becoming overwhelmed.
So far, 3,727 people have tested positive in Kenya and 104 have died in the country of 52 million, according to figures released Monday by Kenya's Ministry of Health. (AP) RS RS